Vector halftoning in an image path utilizing sub-sampled cross-channel image values

ABSTRACT

This disclosure provides methods, apparatus and systems to generate vector halftone data for rendering an image on an image output device. According to one aspect, a method generates vector halftone data as a function of contone pixel data for a given colorant at its nominal resolution and contone pixel data for the other colorants at a relatively lower resolution.

CROSS REFERENCE TO RELATED PATENTS AND APPLICATIONS

U.S. patent application Ser. No. 12/258,871, filed Oct. 27, 2008,entitled “IMAGE PATH UTILIZING SUB-SAMPLED CROSS-CHANNEL IMAGE VALUES,”by Crean et al. is incorporated herein by reference in its entirety.

BACKGROUND

The present disclosure relates to printing from digital images andparticularly color printing. Color printing is typically accomplished bydeposition of multiple colorants as for example, by printers utilizingcyan, magenta yellow and black colorants, where each colorant isrepresented in a channel of the digital image.

Vector halftoning is well suited for ink jet marking because the tightcolor-to-color registration capabilities can be used by the halftoningmethod to produce finer textures and a better gamut by utilizingcorrelation between the halftoned color planes. The methodpreferentially creates dot-off-dot halftone planes, which leads to thoseknown image quality benefits. Vector halftoning requires knowledge ofthe values within multiple color separations to decide on markingdecision in each separation. This is not an issue for many ink jetprinters because jets for the various colorants are in close proximityso image data being printed for any one channel is close to image databeing printed for another channel. The proximity allows for relativelylow cost memory buffers.

Vector halftoning in an image path that has imaging stations for thedifferent colorant planes at a significant separation, however, isexpensive due to the need to provide large page buffers to align thedata for the color planes because the different colorant values (CMYK .. . ) for a given pixel can be printed at significantly different times.In terms of memory capacity and system architecture, such processing isprohibitively expensive and otherwise impractical.

Vector halftoning could be performed in a Digital Front End (DFE) thatprovides the digital image to the printer. Typically, a DFE rasterizesthe image from some page description language form and holds all colorplanes in memory simultaneously. Halftoning in the DFE avoids the costassociated with large amounts of high speed memory in the printer, whichwould be needed if the imaging stations are at a significant distance.However, the approach of halftoning in the DFE results in a seriouslimitation in the ability to maintain the calibration of a print engine.To maintain the calibration of a printer, it is desirable to applyadjustments to the digital values in the color channels to track thephysical marking characteristics of a print engine as it varies in time.Continuous tone pixel values, such as 8 bit (0 to 255) values can beadjusted to maintain the calibration of the overall printing process.After halftoning is performed, pixel values within the channels aretypically binary (0,1), and minor adjustment of a pixel level is verydifficult to perform.

Co-pending patent application Ser. No. 12/258,871, filed Oct. 27, 2008,entitled “Image Path Utilizing Sub-Sampled Cross-Channel Image Values,”by Crean et al., describes an image path architecture for performingcost-effective cross-channel image processing. For generating the outputvalue of a given colorant (e.g., cyan), the method utilizes pixel datafor that colorant at its nominal (full) resolution, while pixel data forother colorants is utilized at a lowered resolution. For instance,color-corrected pixel values for cyan can be obtained by inputting cyanpixel values at nominal resolution into a multi-dimensional LUT, and thevalues for the other color dimensions are input using sub-sampledvalues, such as JPEG DC coefficients or DRI pixel values (DisplayResolution Image). Using the nominal (full) resolutions forcross-channel processing would require a 300% increase in bandwidth foreach output color, while the aforementioned disclosure utilizes JPEG DCcoefficients requiring only a 4% increase. Similar gains are obtained inimage buffering.

The disclosed embodiments, which relate to vector halftoning in an imagepath utilizing sub-sampled cross-channel image values, have thepotential to provide even greater savings in image paths utilizing morethan 4 colorants.

INCORPORATION BY REFERENCE

The following patents and patent publications are totally incorporatedherein by reference in their entirety.

U.S. Patent Application Publication No. 2006/0268294, published Nov. 30,2006, entitled “COLOR PRINTING,” by Snyder et al.

U.S. Patent Application Publication No. 2006/0268295, published Nov. 30,2006, entitled “COLOR PRINTING,” by Yao et al.

U.S. Patent Application Publication No. 2008/0062441, published Mar. 13,2008, entitled “DYNAMIC ADJUSTMENT OF RASTER IMAGE PROCESSINGPERFORMANCE BASED ON COLORS SEEN WITHIN SEVERAL RUNS,” by Nagarajan etal.

U.S. Pat. No. 6,844,941, issued Jan. 18, 2005, entitled “COLORHALFTONING USING A SINGLE SUCCESSIVE-FILLING HALFTONE SCREEN,” by Sharmaet al.

U.S. Pat. No. 6,501,567, issued Dec. 31, 2002, entitled “METHOD ANDSYSTEM FOR DESIGNING SPATIALLY-PARTITIONED AND CORRELATED STOCHASTICSCREENS FOR COLOR HALFTONING,” by Sharma et al.

U.S. Pat. No. 7,136,189, issued Nov. 14, 2006, entitled “COLORHALFTONING USING A MULTI-LEVEL SUCCESSIVE-FILLING HALFTONE SCREENINGALGORITHM,” by Sharma et al.

U.S. Pat. No. 7,095,530, issued Aug. 22, 2006, entitled “COLOR VECTORHALFTONING USING A SUCCESSIVE FILLING WITH IMPROVED COLOR REGISTRATIONLATITUDE,” by Mantell et al.

U.S. Pat. No. 5,631,748, issued May 20, 1997, entitled “COLOR IMAGESHAVING MULTIPLE SEPARATIONS WITH MINIMALLY OVERLAPPING HALFTONE DOTS ANDREDUCED INTERPIXEL CONTRAST,” by Steven J. Harrington.

BRIEF DESCRIPTION

In accordance with the present embodiment, a method is provided forgenerating a halftone data representation of an image for rendering on amulticolor image output device. The method comprises generating a firstcontone pixel data representation of the image for a first colorseparation associated with the image output device and generating asecond contone pixel data representation of the image for a second colorseparation associated with the image output device; generating ahalftone data representation of the image for the first color separationas a function of the first contone pixel data representation at a firstresolution and the second contone pixel data representation at a secondresolution less than the first resolution; generating a halftone datarepresentation of the image for the second color separation; andrendering the image on the multicolor image output device using thehalftone data representation of the image for the first color separationand the halftone data representation of the image for the second colorseparation.

In accordance with another embodiment, a computer program product isprovided comprising a computer-usable data carrier storing instructionsthat, when executed by a computer, cause the computer to perform amethod of generating a halftone data representation of an image forrendering on a multicolor image output device. The method comprisesgenerating a first contone pixel data representation of the image for afirst color separation associated with the image output device;generating a second contone pixel data representation of the image for asecond color separation associated with the image output device;generating a halftone data representation of the image for the firstcolor separation as a function of the first contone pixel datarepresentation at a first resolution and the second contone pixel datarepresentation at a second resolution less than the first resolution;generating a halftone data representation of the image for the secondcolor separation; and rendering the image on the multicolor image outputdevice using the halftone data representation of the image for the firstcolor separation and the halftone data representation of the image forthe second color separation.

In accordance with yet another embodiment, a printing apparatus isprovided comprising an image marking device including a plurality ofcolorants for marking an image on a media substrate, and an imageprocessing device, the image processing device configured to perform amethod of generating a halftone data representation of an image formarking on the image marking device. The method comprises generating afirst contone pixel data representation of the image for a first colorseparation associated with the image marking device; generating a secondcontone pixel data representation of the image for a second colorseparation associated with the image output device; generating ahalftone data representation of the image for the first color separationas a function of the first contone pixel data representation at a firstresolution and the second contone pixel data representation at a secondresolution less than the first resolution; generating a halftone datarepresentation of the image for the second color separation; andrendering the image on the multicolor image output device using thehalftone data representation of the image for the first color separationand the halftone data representation of the image for the second colorseparation.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 is a pictorial schematic of a digital printing system accordingto an exemplary embodiment of this disclosure;

FIG. 2 is a flow diagram of an exemplary process for generating ahalftone data representation of an image according to an exemplaryembodiment of this disclosure.

FIG. 3 is a magnified rendering of an image using independent channel(scaler) halftoning.

FIG. 4 is a magnified rendering of the same image rendered in FIG. 3,where the image is rendered using vector halftoning according to anexemplary embodiment of this disclosure.

FIG. 5 is a schematic illustration of an embodiment of a pixel array.

FIG. 6 is a schematic flow diagram of an embodiment of a procedure forprinting a pixel of print data.

FIG. 7 is a schematic diagram of an embodiment of a stochastic thresholdvalue array.

FIG. 8 is a schematic flow diagram of an embodiment of an alternativestep that can be employed in the procedure of FIG. 6.

DETAILED DESCRIPTION

The present disclosure provides a vector halftoning method and systemthat utilizes pixel data for a given colorant at its nominal (full)resolution, while pixel data for other colorants are utilized at alowered resolution. For instance, halftoned pixel values for cyan can beobtained by inputting cyan pixel values at nominal resolution into avector halftoner, and the values for the other color separations areinput using sub-sampled values, such as JPEG DC coefficients or DRIpixel values (Display Resolution Image). A schematic of an exemplaryembodiment of the present disclosure is shown in FIG. 1.

The sub-sampling rate need not be the same for all channels. Forexample, the human visual system has low acuity for yellow, so the Ychannel could possibly be sampled at a lower resolution than the otherchannels without incurring a significant loss in image quality. Not allchannels need to be passed to each vector halftoning module. Thechannels required by each module are dependent upon the specific vectorhalftoning method that is employed. The sub-sampling could be performedas simple averaging, weighted averaging, decimation or other knownsub-sampling method.

Within the vector halftoning module, the low resolution image data isaligned with the nominal resolution data so pixel-resolution vectorhalftoning can be applied. In effect, the low resolution data is“up-sampled” temporarily within the vector halftoning module. The“up-sampling” could take on a variety of forms, such as using the samelow resolution value repeatedly for a group of co-located nominalresolution pixels, or interpolating between neighboring low resolutionsamples to generate intermediate nominal resolution samples.

The present disclosure applies to halftoning methods that usecross-channel information to make decisions on dot (marked pixel)placement. The term “vector halftoning” is used to describe thesemethods, but different terminology may be used by other practitioners.The exemplary embodiments described herein incorporate a simplehalftoning method as described in Yao and Synder (see U.S. PatentApplication Publication No. 2006/0268294, published Nov. 30, 2006,entitled “COLOR PRINTING”. However, other vector halftoning methods maybe used and are within the scope of this disclosure. For example, U.S.Patent Application Publication No. 2006/0268295, published Nov. 30,2006, entitled “COLOR PRINTING”), the successive fill methods of Sharmaet al. and Mantell et al. (see U.S. Pat. No. 6,844,941, issued Jan. 18,2005, entitled “COLOR HALFTONING USING A SINGLE SUCCESSIVE-FILLINGHALFTONE SCREEN;” U.S. Pat. No. 6,501,567, issued Dec. 31, 2002,entitled “METHOD AND SYSTEM FOR DESIGNING SPATIALLY-PARTITIONED ANDCORRELATED STOCHASTIC SCREENS FOR COLOR HALFTONING”; U.S. Pat. No.7,136,189, issued Nov. 14, 2006, entitled “COLOR HALFTONING USING AMULTI-LEVEL SUCCESSIVE-FILLING HALFTONE SCREENING ALGORITHM”; and U.S.Pat. No. 7,095,530, issued Aug. 22, 2006, entitled “COLOR VECTORHALFTONING USING A SUCCESSIVE FILLING WITH IMPROVED COLOR REGISTRATIONLATITUDE”), the minimal overlap method of Harrington (see U.S. Pat. No.5,631,748, issued May 20, 1997, entitled “COLOR IMAGES HAVING MULTIPLESEPARATIONS WITH MINIMALLY OVERLAPPING HALFTONE DOTS AND REDUCEDINTERPIXEL CONTRAST”).

The images of FIGS. 3 and 4 re intended to show the benefit of a vectorhalftoning method compared to an independent channel (scalar) halftoningmethod. The image in FIG. 3 was halftoned in a channel-independentmanner, which resulted in more dot-on-dot pixels than what occurs in theimage in FIG. 4, which was halftoned using vector processing. Thedot-on-dot structure makes the texture appear grainier and reduces thesize of the printer's color gamut compared to the dot-off-dot structuresthat are produced with the vector method.

Referring to FIG. 1, a digital printing system is indicated generally.This is an example of a network and printing system 10, and includes ascanner 12, an optional computer terminal 14, and a network comprisingterminals 16, 18, 20 connected with other components such as a mainframecomputer 22 all of which are operatively connected through a network 24to an image processor which may include the digital front end (DFE)indicated by reference numeral 26 which provides a digital image outputto a print engine 28. The DFE has memory and a processor for storing andexecuting instructions for providing the described functionality, forexample multichannel sub-sampling.

Referring to FIG. 2, the operations of the image processor 26 are shownpictorially wherein the contone input pixel values for the individualcolorants such as cyan (C), magenta (M), yellow (Y) and black (K) areinputted respectively along lines 32, 34, 36, 38 simultaneously to thesub-sampler 30 and individually to a multi-channel processing unitsdenoted respectively 40, 42, 44, 46. Notably, according to thisdisclosure, the multi-channel processing unit/units apply vectorhalftoning processes to the input contone pixel values. To obtain thecolor separation output values for a given pixel the sub-sampler isoperative to provide a sub-sample of the full resolution pixel valuedata about that pixel for each colorant respectively and inputs thesub-samples respectively to the multi-channel processors for each of theother colorants employed. The multi-channel processors 40, 42, 44, 46are operative to combine the full resolution pixel value respectivelyfor the selected colorant inputted directly thereto along with thesub-sampled low resolution pixel value data for the other colorants toprovide a respective halftone output pixel value indicated respectivelyas C_(o), M_(o), Y_(o) and K_(o) in FIG. 2.

The low resolution sub-sample about a given pixel is obtained for eachcolorant by calculating averages of N×N windows in the image and it hasbeen found satisfactorily to use N=8, but it will be understood thatother values can be employed depending upon the application, and thewindow need not be symmetric in size. The low resolution sub-sampleabout a given pixel may also be obtained by regular sub-sampling pickingone pixel value out of the set of N×N pixels in the window, which isalso known as decimation. Alternatively, averaging with weighted valuesprior to sampling may be employed to derive the sub-samples from thecolor separations. Other order-statistic methods may be used to derivethe sub-samples, such as using the maximum value, median value, orminimum value within the N×N window as the sub-sample value. Anotheralternative is to use the value derived as a result of other operationssuch as JPEG compression which calculates the DC value of every 8×8pixel window. Considering, for example, a sub-sampling process thatutilizes averaging, if the printing engine is processing the cyan valueC at full resolution, it will have averages for M, K and Y across thecorresponding N×N window in which the cyan pixel is located. Thus, ifthe full resolution pixel C has a spatial location in row n and column mof the image, when a factor N=8 is being used for sub-sampling, theprint engine will have available the spatially averaged M value of theblock going from row 8×┌n/8┐−7 to row 8×┌n/8┐ and from column 8×┌m/8┐−7to column 8×┌m/8┐, and correspondingly for the averages of the K and Ysub-sample pixel values.

Printing is accomplished by selectively printing, depositing, applyingor otherwise forming markings such as dots on a receiver surface orsubstrate that can be a print output medium such as paper or a transfersurface such as a transfer belt or drum. If a transfer surface is used,the image formed or printed on the transfer surface is appropriatelytransferred to a print output medium such as paper.

FIG. 5 is a schematic illustration of an embodiment of an array 80 ofpixel locations P that can be used to define the locations on a printoutput medium 81 that can be marked or printed. A marking of aparticular primary colorant (e.g., cyan, magenta, yellow or black) thatis printed or deposited at a pixel location can be conveniently called adot.

Each pixel location P can, for example, be marked or printed with (a)one or more non-black primary colorant dots (e.g., cyan, magenta oryellow), (b) a black dot by itself, or (c) a black dot and at least onenon-black primary colorant dot.

Print data typically comprises continuous tone data (such as 32-bit or24-bit pixel data for the collective colorant separations), andhalftoning (e.g., using one or more halftone threshold arrays) iscommonly employed to map or transform continuous tone data to ahalftoned bit map that contains one bit per pixel per primary colorantplane, for example.

FIG. 6 is a schematic flow diagram of an embodiment of a vectorhalftoning procedure for printing a pixel of CMYK print data. At 111cyan, magenta, yellow, and black input color values C₁, M₁, Y₁, K₁ arereceived. At 113 the input color values C₁, M₁, Y₁, K₁ are transformedto cyan, magenta, and yellow color values C, M, Y, for example in such amanner that each of C, M, Y is not greater than a predetermined maximumcolor value such as 255 (for example for 8-bit color values):C=C ₁ +K ₁M=M ₁ +K ₁Y=Y ₁ +K ₁

-   If C>255, set C=255-   If M>255, set M=255-   If Y>255, set Y=255

At 115, a blue colorant value B for overlapping cyan and magenta isinitialized to zero (0), and the cyan and magenta output colorant valuesC_(out), M_(out) are initialized to the cyan and magenta values C, M:B=0C _(out) =CM _(out) =M

At 117, a determination is made as to whether C+M is greater than 255.If no, processing continues at 121.

If the determination at 117 is yes, at 119 values for B, C_(out), andM_(out) are calculated, for example such that B+C_(out)+M_(out)=255:B=C+M−255C _(out)=255−MM _(out)=255−C

The equation B+C_(out)+M_(out)=255 is based on having no white spacesince C+M>255. The Equation B=C+M−255 identifies the overlapping cyanand magenta dots as being the amount of C+M that exceeds 255. Theforegoing exemplary expressions for C_(out) and M_(out) also satisfy theequations C=B+C_(out) and M=B+M_(out), which can provide for printing ofthe total number of cyan and magenta dots requested by the CMYK colordata.

At 121 halftoning is performed using the following, for example using astochastic halftone threshold array A1 having a threshold value t foreach pixel scaled to [0, 255] for blue, cyan and magenta, and astochastic halftone threshold array A2 having a threshold value t′ foreach pixel scaled to [0, 255], for the illustrative example wherein thepredetermined maximum color value is 255.

If B>t, cyan, magenta dots are on Else if B+C_(out)>t, cyan dot is onElse if B+C_(out)+M_(out)>t, magenta dot is on If Y>t’, yellow dot is on

FIG. 7 schematically illustrates an embodiment of a stochastic halftonethreshold array that can be employed as either or both of the thresholdarrays A1, A2.

The threshold arrays A1, A2 can be correlated or uncorrelated. By way ofillustrative example, the threshold array A2 can be derived by shiftingthe threshold array A1 by a predetermined number of pixels, whereby thethreshold array A2 is a replica of the threshold array A1 that isshifted relative to the threshold array A1 by a predetermined number ofpixels. Where A2 is a shifted version of A1, the correlation between A2and A1 decreases as the shift increases.

FIG. 8 sets forth an embodiment of an alternative halftoning step 221′that can be substituted 221 in the procedure of FIG. 6:

If B>t, cyan, magenta dots are on Else if B+M_(out)>t, magenta dot is onElse if B+ M_(out)+C_(out)>t, cyan dot is on If Y>t’, yellow dot is onSuch halftoning can be performed, for example, using a stochastichalftone threshold array A1 having a threshold value t for each pixelscaled to [0, 255] for blue, cyan and magenta, and a stochastic halftonethreshold array A2 having a threshold value t′ for each pixel scaled to[0, 255] for yellow, for the illustrative example wherein thepredetermined maximum color value is 255. FIG. 7 schematicallyillustrates an embodiment of a stochastic halftone threshold array thatcan be employed as either or both of the threshold arrays A1, A2.

It should be appreciated that the foregoing generally contemplatesprocessing CMY print data, where such data can be transformed from CMYKdata. To the extent that the input print data comprises CMY print data,K₁ can be omitted from the equations at 113 where the input color valuesC₁, M₁, Y₁ are transformed to cyan, magenta, and yellow color values C,M, Y, for example in such a manner that each of C, M, Y is not greaterthan a predetermined maximum color value such as 255 (for example for8-bit color values).

Pursuant to the disclosed procedures for processing color values, cyanand magenta dots are substantially uniformly distributed, andoverlapping cyan and magenta dots are reduced.

In the halftoning step 219′, the threshold arrays A1, A2 can becorrelated or uncorrelated. By way of illustrative example, thethreshold array A2 can be derived by shifting the threshold array A1 bya predetermined number of pixels, whereby the threshold array A2 is areplica of the threshold array A1 that is shifted relative to thethreshold array A1 by a predetermined number of pixels. Where A2 is ashifted version of A1, the correlation between A2 and A1 decreases asthe shift increases.

The sub-sampling module 30 may utilize a simple averaging over thesub-sample area or other sub-sampling methods such as decimation,weighted averaging and non linear maximum, minimum and mediansub-sampling may be used. If weighted averaging is used within a commonsub-sampler, a common memory buffer for the weights that are applied toall the channels may be employed. An alternative arrangement wouldpermit the sub-sampler to be adaptive such that different sub-samplingrates are used for the image data with different levels of complexity.In addition to sub-sampling, additional compression can be applied tothe low resolution channels thereby further reducing the band widthrequired of the cross panel process.

Alternatively, the sub-sample value can be derived as a result of otheroperations such as JPEG compression which calculates the DC value ofevery 8×8 pixel window. Thus, if the printing engine is processing thecyan value C at full resolution, it will have averages for M and Yacross the corresponding N×N window in which the cyan pixel is located.Thus, if the full resolution pixel C has a spatial location in row n andcolumn m of the image, when a factor N=8 is being used for sub-sampling,the print engine will have available the spatially averaged M value ofthe block going from row 8×┌n/8┐−7 to row 8×┌n/8┐ and from column8×┌m/8┐−7 to column 8×┌m/8┐, and correspondingly for the averages of theK and Y sub-sample pixel values.

Another alternative is to employ JPEG2000, which is a common imagecompression format, as a source of sub-sampled image data. JPEG2000transforms the image into a set of two dimensional sub-band signals,each representing the activity of the image in various frequency bandsat various spatial resolutions. Each successive decomposition level ofthe sub-bands has approximately half the horizontal and half thevertical resolution of the previous level. A reverse decompositionmodule within the sub-sampler reverses as many decomposition steps asnecessary to obtain a low resolution version of the original image withresolution equal to the desired sub-sample spatial resolution utilizedin the multi-dimensional mappings.

Yet another alternative is to use a sampler whose output is designed toproduce a display resolution image, or a “thumbnail” view of the image.

In the present practice, it has been found satisfactory to employ asub-sample of 1 out of 64 for an 8×8 pixel cell and 1 out of 256 for a16×16 pixel cell for the colorants other than the selected colorant forfull resolution.

The teachings herein have described an image path utilizing sub-sampledcross-channel image values using cyan, magenta, yellow and black asexemplary colorants. However, it has been found satisfactory for usewith other colorants and colorant combinations, and particularly forprinting systems employing more than four colorants. For example, somecombination of gray, light cyan, light magenta, and dark yellowcolorants, along with CMYK are used in certain printer to achieve asmoother appearance in image highlights. Orange, green and violetcolorants are used in some printing systems for purposes of extendingthe gamut of achievable colors of the printer. Other examples ofcolorants that may be employed are red, blue, clear, and white. Otherprinting systems may use fewer colorants, such as a highlight colorprinter that prints black and one color.

It will be appreciated that various of the above-disclosed and otherfeatures and functions, or alternatives thereof, may be desirablycombined into many other different systems or applications. Also thatvarious presently unforeseen or unanticipated alternatives,modifications, variations or improvements therein may be subsequentlymade by those skilled in the art which are also intended to beencompassed by the following claims.

1. A method of generating a halftone data representation of an image forrendering on a multicolor image output device comprising: (a) generatinga first contone pixel data representation of the image for a first colorseparation associated with the image output device; (b) generating asecond contone pixel data representation of the image for a second colorseparation associated with the image output device; (c) generating ahalftone data representation of the image for the first color separationas a function of the first contone pixel data representation at a firstresolution and the second contone pixel data representation at a secondresolution less than the first resolution; (d) generating a halftonedata representation of the image for the second color separation; and(e) rendering the image on the multicolor image output device using thehalftone data representation of the image for the first color separationand the half-tone data representation of the image for the second colorseparation.
 2. The method according to claim 1, wherein step (d)comprises: generating a halftone data representation of the image forthe second color separation as a function of the first contone pixeldata representation and the second contone pixel data representation. 3.The method according to claim 2, wherein step (d) comprises: generatingthe halftone data representation of the image for the second colorseparation as a function of the first contone pixel data representationat a third resolution and the second contone pixel data representationat a fourth resolution greater than the third resolution.
 4. The methodaccording to claim 3, further comprising: generating one or moreadditional contone pixel data representations of the image for one ormore, respective, additional color separations associated with the imageoutput device; generating one or more halftone data representations ofthe image for the respective one or more additional color separations;and rendering the image on the multicolor image output device using thehalftone data representation of the image for the first colorseparation, the halftone data representation of the image for the secondcolor separation, and the halftone data representation of the image forthe one or more additional color separations.
 5. The method according toclaim 4, wherein the one or more halftone data representations of therespective one or more additional color separations are generated as afunction of one or more of the other color separations represented incontone at a reduced resolution relative to the contone resolution ofthe respective additional color separation.
 6. The method according toclaim 1, wherein step (a) generates the first contone pixel datarepresentation at a first nominal resolution, step (b) generates thesecond contone pixel data representation at a second nominal resolution,and step (c) generates the halftone data representation of the image forthe first color separation as a function of the first contone pixel datarepresentation at the first nominal resolution and the second contonepixel data representation at a resolution less than the second nominalresolution.
 7. The method according to claim 6, wherein the first andsecond nominal resolutions are equivalent.
 8. The method according toclaim 1, wherein the second contone pixel data representation at aresolution less than the second nominal resolution is generated bysub-sampling the second contone pixel data representation at the secondnominal resolution.
 9. The method according to claim 8, wherein thesub-sampling includes one of (a) simple averaging over a sub-samplearea, (b) weighted averaging over a sub-sampled area, (c) determiningthe median of pixel values in a sub-sampled area, (d) determining theminimum of pixel values in a sub-sampled area, (e) determining themaximum of pixel values in a sub-sampled area, and (f) decimation.
 10. Acomputer program product comprising: a non-transitory computer-usabledata carrier storing instructions that, when executed by a computer,cause the computer to perform a method of generating a halftone datarepresentation of an image for rendering on a multicolor image outputdevice, the method comprising: (a) generating a first contone pixel datarepresentation of the image for a first color separation associated withthe image output device; (b) generating a second contone pixel datarepresentation of the image for a second color separation associatedwith the image output device; (c) generating a halftone datarepresentation of the image for the first color separation as a functionof the first contone pixel data representation at a first resolution andthe second contone pixel data representation at a second resolution lessthan the first resolution; (d) generating a halftone data representationof the image for the second color separation; and (e) rendering theimage on the multicolor image output device using the halftone datarepresentation of the image for the first color separation and thehalftone data representation of the image for the second colorseparation.
 11. The computer program product according to claim 10,wherein step (d) comprises: generating a halftone data representation ofthe image for the second color separation as a function of the firstcontone pixel data representation and the second contone pixel datarepresentation.
 12. The computer program product according to claim 11,wherein step (d) comprises: generating the halftone data representationof the image for the second color separation as a function of the firstcontone pixel data representation at a third resolution and the secondcontone pixel data representation at a fourth resolution greater thanthe third resolution.
 13. The computer program product according toclaim 12, wherein the method comprises: generating one or moreadditional contone pixel data representations of the image for one ormore, respective, additional color separations associated with the imageoutput device; generating one or more halftone data representations ofthe image for the respective one or more additional color separations;and rendering the image on the multicolor image output device using thehalftone data representation of the image for the first colorseparation, the halftone data representation of the image for the secondcolor separation, and the halftone data representation of the image forthe one or more additional color separations.
 14. The computer programproduct according to claim 13, wherein the one or more halftone datarepresentations of the respective one or more additional colorseparations are generated as a function of one or more of the othercolor separations represented in contone at a reduced resolutionrelative to the contone resolution of the respective additional colorseparation.
 15. The computer program product according to claim 13,wherein step (a) generates the first contone pixel data representationat a first nominal resolution, step (b) generates the second contonepixel data representation at a second nominal resolution, and step (c)generates the halftone data representation of the image for the firstcolor separation as a function of the first contone pixel datarepresentation at the first nominal resolution and the second contonepixel data representation at a resolution less than the second nominalresolution.
 16. The computer program product according to claim 15,wherein the first and second nominal resolutions are equivalent.
 17. Thecomputer program product according to claim 13, wherein the secondcontone pixel data representation at a resolution less than the secondnominal resolution is generated by sub-sampling the second contone pixeldata representation at the second nominal resolution.
 18. The computerprogram product according to claim 17, wherein the sub-sampling includesone of (a) simple averaging over a sub-sample area, (b) weightedaveraging over a sub-sampled area, (c) determining the median of pixelvalues in a sub-sampled area, (d) determining the minimum of pixelvalues in a sub-sampled area, (e) determining the maximum of pixelvalues in a sub-sampled area, and (f) decimation.
 19. A printingapparatus comprising: an image marking device including a plurality ofcolorants for marking an image on a media substrate; and an imageprocessing device, the image processing device configured to perform amethod of generating a halftone data representation of an image formarking on the image marking device, the method comprising: (a)generating a first contone pixel data representation of the image for afirst color separation associated with the image marking device; (b)generating a second contone pixel data representation of the image for asecond color separation associated with the image output device; (c)generating a halftone data representation of the image for the firstcolor separation as a function of the first contone pixel datarepresentation at a first resolution and the second contone pixel datarepresentation at a second resolution less than the first resolution;(d) generating a halftone data representation of the image for thesecond color separation; and (e) rendering the image on the multicolorimage output device using the halftone data representation of the imagefor the first color separation and the halftone data representation ofthe image for the second color separation.
 20. The printing apparatusaccording to claim 19, wherein step (d) comprises: generating thehalftone data representation of the image for the second colorseparation as a function of the first contone pixel data representationat a third resolution and the second contone pixel data representationat a fourth resolution greater than the third resolution.
 21. Theprinting apparatus according to claim 19, wherein step (a) generates thefirst contone pixel data representation at a first nominal resolution,step (b) generates the second contone pixel data representation at asecond nominal resolution, and step (c) generates the halftone datarepresentation of the image for the first color separation as a functionof the first contone pixel data representation at the first nominalresolution and the second contone pixel data representation at aresolution less than the second nominal resolution.
 22. The printingapparatus according to claim 19, wherein the second contone pixel datarepresentation at a resolution less than the second nominal resolutionis generated by sub-sampling the second contone pixel datarepresentation at the second nominal resolution.
 23. The printingapparatus according to claim 22, wherein the sub-sampling includes oneof (a) simple averaging over a sub-sample area, (b) weighted averagingover a sub-sampled area, (c) determining the median of pixel values in asub-sampled area, (d) determining the minimum of pixel values in asub-sampled area, (e) determining the maximum of pixel values in asub-sampled area, and (f) decimation.